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FIRST SEMESTER U.G. DEGREE EXAMINATION, NOVEMBER 2022
(CBCSS—UG)
Mathematics
MTS 1B 01—BASIC LOGIC AND NUMBER THEORY
(2019 Admissions)

Two Hours and a Half Maximum Marks : 80

Section A

Answer any number of questions.
Each question carries 2 marks.
Maximum 25 marks.

Evaluate the Boolean expression ~ [(a < b)v (b>c)], where a = 3,b = 5 andc = 6.

Negate the propositions (i) (vx)(x? =x), (ii) (Gx), (x? = x), where the UD = set of integers.
Determine whether or not each is a contradiction :
(i) (pA~(p)), Gi) ~ (pv ~ p).
Prove that there is no positive integer between 0 and 1.
Define recursively the factorial function ‏م‎
‎Find the sum of (111000), and (000111),.
Prove that there are infinitely many primes.
Define Fermat numbers and find the third fermat number.
Prove that any two consecutive Fibonacci numbers are relatively prime.
Is 341 is a pseudo prime ? Justify your answer.

If a=b(modm). Prove that q” =b”"(modm) for any positive integer n.
Determine whether the congruence 8x =10(mod6) is solvable. If so, find the number of
incongruent solutions.
Show that >, %=18.
pot -1
2-1

Let p be any prime and e any positive integer. Prove that © ( °) 7
Evaluate (12, 34, 27, 1087, 97).

( Maximum ceiling 25 marks)

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